A conventional radar determines the range to a target by measuring the round trip time of the returned radar signal. This method of determining the range is typically implemented by detecting the arrival time of the leading edge of the returned signal. The implementation works well as long as the transmission medium produces little or no distortion to the leading edge of the signal. Media such as the atmosphere, empty space, dry ground, solid rock and ice fall into this class of media. However, when the transmission medium contains water, molten rock or hot rock such large signal distortions are produced by the medium that the exact arrival time of the leading edge cannot be determined. Hence, the standard technique for measuring range becomes too inaccurate to be effective. Water with low mineral content and molten rock are examples of media that produce such large signal distortions that the standard method fails. But, in all these cases, range information can be derived by a new method, disclosed herein, that actually makes use of the distortions of the returned signal to determine range.
Determining the range of a scattering or reflecting object by measuring the round-trip time of the leading edge of the radar signal has been known and used throughout the history of radar. The round-trip time .DELTA.T of an electromagnetic signal returned by a scattering or reflecting object is observed, and the range d=c.DELTA.T/2 is derived from the velocity of light c=1/.sqroot..epsilon..mu., where .epsilon. and .mu. are the permittivity and the permeability of the medium. This approach works as long as the conductivity .sigma. of the medium can be ignored, which is the case in the atmosphere, vacuum, dry soil and rock. However, if significant amounts of water are present or if electromagnetic signals are used to probe hot or molten rock, the conductivity .sigma. can no longer be ignored. This means that a) the propagation velocity of a radar signal no longer defined by c=1/.sqroot..epsilon..mu., and b) signals transmitted through such a medium are significantly distorted. The exact arrival time of a pulse that has been distorted so that its leading edge is no longer sharp, is dependent upon the detection level (i.e., threshold level) Hence, the precise round trip time .DELTA.T is difficult to determine. Therefore, range determination by means of the conventional radar principle is no longer feasible.
In order to overcome this difficulty, the propagation of electromagnetic signals in lossy media was studied. This study ran into an unexpected obstacle of great significance. Maxwell's equations, which are the basis for all electromagnetic wave transmission, were found to fail for the propagation of pulses or "transients" in lossy media. Upon investigation, the reason turned out to be the lack of a magnetic current density term analogous to the electric current density term. It is understood that currents are carried by both charges and dipoles and higher order multipoles. For instance, the current in a resistor is carried by charges or monopoles. But, the electric "polarization" current flowing through the dielectric of a capacitor is carried by electric dipoles. A magnetic current density term does not occur in Maxwell's equations because magnetic charges equivalent to negative electric charges (e.g., electrons, negative ions). or equivalent to positive electric charges (e.g. positrons, protons, positive ions) have never been reliably observed. Nevertheless, since magnetic dipoles are known to exist (e.g., the magnetic compass needle), there must be magnetic polarization currents carried by these dipoles. This fact calls for a magnetic current density term in Maxwell's equations.
The modification of Maxwell's equations and the transient solutions derived from the modified equations are discussed in H. F. Harmuth, Propagation of Nonsinusoidal Electromagnetic Waves, Academic Press, New York 1986, which is hereby incorporated by reference. Using these solutions, the propagation and distortion of electromagnetic signals was further studied in the PhD thesis "Propagation Velocity of Electromagnetic Signals in Lossy Media in the Presence of Noise", by R. N. Boules, Department of Electrical Engineering, The Catholic University of America, Washington D.C., 1989. This thesis contains computer plots of distorted signals having propagated over various distances in lossy media with a conductivity .sigma.. In particular, the case .sigma.=4S/m, relative permittivity 80, and relative permeability 1 (i.e., typical values for sea water) is treated in some detail.